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We consider an optimization problem related to mass transportation:\udgiven two probabilities f þ and f  on an open subset WHRN, we let vary the cost of the\udtransport among all distances associated with conformally flat Riemannian metrics on W\udwhich satisfy an integral constraint (precisely, an upper bound on the L1-norm of the Riemannian\udcoe‰cient). Then, we search for an optimal distance which prevents as much as\udpossible the transfer of f þ into f : higher values of the Riemannian coe‰cient make the\udconnection more di‰cult, but the problem is non-trivial due to the presence of the integral\udconstraint. In particular, the existence of a solution is a priori guaranteed only on the\udrelaxed class of costs, which are associated with possibly non-Riemannian Finsler metrics.\udOur main result shows that a solution does exist in the initial class of Riemannian\uddistances

Optimal Riemannian distances preventing mass transfer